docs: def Froude_densimetric(V, L, rho1, rho2, heavy=True, g=g):
      r'''Calculates the densimetric Froude number :math:`Fr_{den}` for velocity
      `V` geometric length `L`, heavier fluid density `rho1`, and lighter fluid 
      density `rho2`. If desired, gravity can be specified as well. Depending on
      the application, this dimensionless number may be defined with the heavy
      phase or the light phase density in the numerator of the square root.
      For some applications, both need to be calculated. The default is to 
      calculate with the heavy liquid ensity on top; set `heavy` to False
      to reverse this.
  
      .. math::
          Fr = \frac{V}{\sqrt{gL}} \sqrt{\frac{\rho_\text{(1 or 2)}} 
          {\rho_1 - \rho_2}}
  
      Parameters
      ----------
      V : float
          Velocity of the specified phase, [m/s]
      L : float
          Characteristic length, no typical definition [m]
      rho1 : float
          Density of the heavier phase, [kg/m^3]
      rho2 : float
          Density of the lighter phase, [kg/m^3]
      heavy : bool, optional
          Whether or not the density used in the numerator is the heavy phase or
          the light phase, [-]
      g : float, optional
          Acceleration due to gravity, [m/s^2]
  
      Returns
      -------
      Fr_den : float
          Densimetric Froude number, [-]
  
      Notes
      -----
      Many alternate definitions including density ratios have been used.
  
      .. math::
          Fr = \frac{\text{Inertial Force}}{\text{Gravity Force}}
          
      Where the gravity force is reduced by the relative densities of one fluid
      in another.
      
      Note that an Exception will be raised if rho1 > rho2, as the square root
      becomes negative.
  
      Examples
      --------
      >>> Froude_densimetric(1.83, L=2., rho1=800, rho2=1.2, g=9.81)
      0.4134543386272418
      >>> Froude_densimetric(1.83, L=2., rho1=800, rho2=1.2, g=9.81, heavy=False)
      0.016013017679205096
  
      References
      ----------
      .. [1] Hall, A, G Stobie, and R Steven. "Further Evaluation of the 
         Performance of Horizontally Installed Orifice Plate and Cone 
         Differential Pressure Meters with Wet Gas Flows." In International 
         SouthEast Asia Hydrocarbon Flow Measurement Workshop, KualaLumpur,
         Malaysia, 2008.
      '''
      if heavy:
          rho3 = rho1
      else:
          rho3 = rho2
      return V/((g*L)**0.5)*(rho3/(rho1 - rho2))**0.5